For solving the aforementioned problem, we consider a practical case that prior distribution parameters of the device state matrix \(\mathbf {X}\)  are unknown, which is modeled as a Bernoulli-Gaussian mixture distributed random matrix. Note that this is a general and accurate distribution for the practical scenarios with a large-scale antenna array at the BS [1]}. Since the transformed device state matrix \(\mathbf {S}\)  has the same distribution parameters with \(\mathbf {X}\) , the distribution of the transformed device state matrix can be specifically expressed as
\(p(\mathbf {S})=\prod _{n=1}^{N}\prod _{r=1}^{r^e}(1-\epsilon _{nr} )\delta (s_{nr})+\epsilon _{nr} \sum \limits _{j = 1}^J {q_{nj}\mathcal {CN}({s_{nr}};0,\vartheta _{nj}^2)},\) 
